Improved bounds in the metric cotype inequality for Banach spaces

Ohad Giladi, Manor Mendel, Assaf Naor

פרסום מחקרי: פרסום בכתב עתמאמרביקורת עמיתים


It is shown that if (X,||·||X) is a Banach space with Rademacher cotype q then for every integer n there exists an even integer m≲n1+1/q such that for every f:Zmn→X we have. where the expectations are with respect to uniformly chosen x∈Zmn and ε∈{-1,0,1}n, and all the implied constants may depend only on q and the Rademacher cotype q constant of X. This improves the bound of m≲n2+1q from Mendel and Naor (2008) [13]. The proof of (1) is based on a "smoothing and approximation" procedure which simplifies the proof of the metric characterization of Rademacher cotype of Mendel and Naor (2008) [13]. We also show that any such "smoothing and approximation" approach to metric cotype inequalities must require m≳n1/2 + 1/q.

שפה מקוריתאנגלית
עמודים (מ-עד)164-194
מספר עמודים31
כתב עתJournal of Functional Analysis
מספר גיליון1
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 1 ינו׳ 2011

הערה ביבליוגרפית

Funding Information:
O.G. was partially supported by NSF grant CCF-0635078. M.M. was partially supported by ISF grant no. 221/07, BSF grant no. 2006009, and a gift from Cisco research center. A.N. was supported in part by NSF grants CCF-0635078 and CCF-0832795, BSF grant 2006009, and the Packard Foundation.

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